Question

What is the force experienced by a semicircular wire of radius $R$ when it is carrying a current $I$ and is placed in a uniform magnetic field of induction $B$ as shown in figure?

• A. Zero
• B. $2IRB$
• C. $IRB$
• D. $2\pi IRB$

Answer 1

The correct option is A Zero


Magnetic force, $\overrightarrow{F}=I(\overrightarrow{l}\times \overrightarrow{B})$

Except point $C$, the length vector $\overrightarrow{l}$ along the direction of current $I$ are symmetry about the point $C$.

These symmetry elements will lead to the force on the wire which are equal in magnitude but opposite in direction.

Thus, the net force will be zero on the wire.

At point $C$, vector $\overrightarrow{l}$ is parallel to the magentic field $\overrightarrow{B}$ so, the force at this point also be zero.

Hence, the net force on the wire will be zero.
So, option (a) is the correct answer.